You are required to move your .com domain name to a .co.uk or an other country specific TLD (top level domain). How will this impact your rankings in the short and long term over at the #1 search engine, Google? Good question. A thread at WebmasterWorld named .com -> .co.uk site transition discusses this topic.
The basic steps one should take is the classic 301 redirects from the old pages to the new pages. Do your best to ask people who have linked to you to link to the new URLs. Make sure all your directory listings have been updated correctly. And wait it out.
One member gives reassuring words "I have done exactly the same in the past and it has worked perfectly."